Geodesic
On Regular Anti-congruence in Anti-ordered Semigroups
Publications de l'Institut Mathématique, _N_S_81 (2007) no. 95, p. 95 .

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For an anti-congruence $q$ we say that it is regular anti-congruence on semigroup $(S,=,\neq,\cdot,\alpha)$ ordered under anti-order $\alpha$ if there exists an anti-order $\theta$ on $S/q$ such that the natural epimorphism is a reverse isotone homomorphism of semigroups. Anti-congruence $q$ is regular if there exists a quasi-antiorder $\sigma$ on $S$ under $\alpha$ such that $q=\sigma\cup\sigma^{-1}$. Besides, for regular anti-congruence $q$ on $S$, a construction of the maximal quasi-antiorder relation under $\alpha$ with respect to $q$ is shown.
DOI : 10.2298/PIM0795095R
Classification : 03F65 06F05 20M10
Keywords: Constructive mathematics, semigroup with apartness, anti-ordered semigroup, anti-congruence, regular anti-congruence, quasi-antiorder 
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     title = {On {Regular} {Anti-congruence} in {Anti-ordered} {Semigroups}},
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Daniel Romano. On Regular Anti-congruence in Anti-ordered Semigroups. Publications de l'Institut Mathématique, _N_S_81 (2007) no. 95, p. 95 . doi : 10.2298/PIM0795095R. http://geodesic.mathdoc.fr/articles/10.2298/PIM0795095R/

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